Miles from the Las Vegas strip, along a dusty highway flanked by barbed-wire fences and strip malls, Sin City harbours an unexpected secret: a museum devoted to words. But of the three taxi drivers and two hotel concierges I ask for directions, not one has heard of the museum.

It's amazing anybody could miss the Neon Boneyard Museum, which at first glance resembles a Scrabble set designed for a giant. The metal tips of lorry-sized words peak out over the fences of a huge industrial lot – the curl of an "S" visible through the barriers, the peeling paint of an obese red "B" glinting. This is where the neon signs of Las Vegas come to die, forming a higgledy-piggledy poem to the city's history. Spanning from early neon offerings of "beer" and "girls" through to the atomic font of the cold war, this is Vegas in her own words. "Literary tours" might not be advertised in this city's neon, but fiction is everywhere in Las Vegas.

When I ask a taxi driver to take me from the Neon Boneyard to the nearest library, he nervously replies: "You mean the Library strip joint on Boulder Avenue?" Vegas might be a literary inspiration, but the most popular "Library" in Vegas involves strippers wearing glasses.

Instead I end up in a carousel-shaped ice cream parlour spinning above a circus-themed mega casino. It is here, rotating above bleary-eyed gamblers at roulette wheels and surrounded by sugar-hyped kids winning stuffed bears at arcade games, that Hunter S Thompson places the "vortex" and "main nerve" of the American Dream in Fear and Loathing in Las Vegas. The same carousel horses have been marching over Circus Circus since it opened in 1968, but while the character in Fear and Loathing sipped Wild Turkey to take the edge off his mescaline high, I suck sugary vanilla ice cream off a miniature purple spoon. The "main nerve" of the American dream has become an ice cream parlour.

"Hunter would be disgusted, right?" says a man's voice. I look up from my copy of Fear and Loathing to see that my literary tour guide for the evening has turned up. Local journalist and author of Beneath the Neon, Matthew O'Brien has bought himself a Slurpee – although you get the sense he'd rather have a whiskey – and sits down next to me. "All these arcade games would have been the same, though," he says, sweeping his hand over our surroundings and taking my book off me. "Shoot the pasties off the nipples of a 10ft bull dyke and win a cotton-candy goat?" he reads from a marked passage.

"An orangutan named Boobie used to wander around Circus Circus in the 1960s and Hunter tried to buy him for $800," Matthew adds as we watch a trapeze artist spin from the rafters. Matthew interviewed Thompson over the phone a few times and was supposed to meet him the weekend that the movie of Fear and Loathing premiered in Vegas, but Thompson never turned up.

"He called me a few days before," says Matthew, "and asked me to buy him a miniature fridge for the weekend, along with a copy of The Rise and Fall of the Third Reich. In Fear and Loathing he describes Circus Circus as what everyone would have been doing on a Saturday night if the Nazis had won the war."

Anna Stothard and Elvis

Nightmares and dreams fill the literature of Las Vegas – from Thompson's hallucinogenic American Dreams to the sci-fi speculations of Stephen King's post-apocalyptic epic The Stand and JG Ballard's Hello America. Vegas, after all, has dreaming at its roots. In 1945 the gangster Bugsy Siegel drove from LA through the Mojave Desert, fantasising about turning an isolated desert town into a sin city where celebrities and reprobates would flock. Take a trip outside the city today, to Hoover Dam or the pink-tinted mountains of Red Rock, and from afar you'll see what a bold dream this was: the neon city appears like a mirage inside a huge puddle of dust. Bugsy's dream quickly became a nightmare, and while he finished the first mega casino in Vegas in 1946, he was shot dead by rival gangsters a year later. A bronze plaque commemorates Bugsy today in front of the Flamingo wedding chapel.

"It lay in the middle of the desert like some improbable gem," writes Stephen King in The Stand, where America's population is nearly annihilated and survivors join two camps: good and evil. No prizes for guessing where evil congregates.

As Matthew and I leave Circus Circus for the Strip, waving goodbye to the cross-eyed neon clown that guards the big top, Las Vegas looks like something Stephen King might have invented rather than just riffed on. Matthew points out replica Venetian bridges, an Eiffel Tower, a pop-art parody of Venus de Milo, a glinting black-glass Egyptian pyramid, all hovering in an eerie neon glow and rising up in a heat that burns the soles of your feet through your shoes and melts your nail polish.

We disembark at the entrance of the MGM Grand, where the finale of The Stand takes place "on the steps leading up to the lobby doors… where incoming guests had once parked while the doorman whistled up a bellhop". Cheered on by an excited "crowd-animal" of spectators, it was here that King's anti-hero readied himself to execute his enemies just moments before a madman drags a nuclear bomb into town and explodes the city.

Matthew and I stand in the entrance to one of the largest hotels in the world, containing 18,000 doors, 7,778 beds and 93 lifts, watching a "crowd-animal" of tourists, and we agree that while it doesn't take much to imagine Vegas as the catalyst for apocalypse, the sheer exuberance and cheek of the city is nothing short of spectacular.

"It was an excess of fantasy that killed the old United States," prophesies JG Ballard in Hello America, where nomad explorers find android replicas of celebrities dancing in a deserted casino – but fantasy doesn't seem to have killed Vegas yet.

Matthew and I head downtown to Fremont Street, where I dance with three drunk Elvis impersonators under the awning of the Golden Nugget Casino. While the strip feels futuristic, downtown is gangster, old-school, local. The best alternative hangouts in Vegas are also down here, among bedraggled celebrity impersonators and low-rollers. The Griffin and a renovated beauty parlour called the Beauty Bar are the dives for meeting local artists and singers at night, while the Beat Coffeehouse and the Arts Factory are the places to curl up with a book and a hangover during the day.

As our night draws to a close, Matthew raises his eyebrows on dropping me off at a hotel called El Cortez, near Fremont Street. "El Cortez has a very particular smell," he says, which is true, but this low-ceilinged and smoke-clogged casino turns out to be one of my favourite locations in Vegas. It's one of the oldest hotels in the city, and the only one where you can play slots with real quarters rather than fake casino cash.

In the casino bar, drinking a whiskey sour while two middle-aged women with painted-on eyebrows discuss slot-machine etiquette, I begin to read the latest literary sensation to come out of Vegas, Charles Bock's Beautiful Children.

Bock is the poster boy for contemporary Las Vegas literature, and much of Beautiful Children – a New York Times bestseller described by Esquire as "dirty, fast and hypnotic" – plays out in the city's shady perimeters and suburbs, where the strip is nothing but a "distant row of glowing toys". Bock himself is a Vegas local, and his story follows a spoilt suburban kid as he gets lost in the "crown jewel of a country that has institutionalised indulgence"; a nightmare world populated with local desert punks, dwarves, suburban mothers, comic-book geeks and surgically bloated strippers. Bock's fictional stripper, Cheri Blossom, controls men with the ease of "cutting away the mealy part of an apple that had been left on top of the fridge overnight", and I look up from my pages to see a vixen with 6in stilettos kiss the bald head of a man hunched in an oxygen-tank laden wheelchair. Forget tigers and comedy acts – if you see one show in Vegas, it should be people-watching at El Cortez.

"You see some weird things growing up in Vegas," Bock told me on the phone. "Our weekend family lunch was an all-you-can-eat buffet in a casino; Vegas kids cut class to gamble away their pocket money."

According to Alissa Nutting, another local Vegas author who recently published her first book of short stories, Unclean Jobs for Women and Girls, "Vegas is a micro and macrocosm of every worthwhile fictional plot known to man – it all plays out here daily. It's just in the air."

In this fantasy city even the local low-rollers are dreamers, pushing their wages on to red and holding their breath. Elvises drinking in the street, burlesque dancers kicking feathers in downtown dive bars, hotel valets moonlighting as country and western singers in vintage casinos at night – alternate reality rules this city. "You don't forget watching someone in a veil and a 'bride-to-be' jacket, on her knees throwing up into a sidewalk grate while Japanese tourists take photos," says Nutting.

The city might be greedy and sweaty. It might even be like holidaying in the post-apocalyptic vortex of the American Dream, but one thing's for sure: you certainly won't forget the stories you find in Sin City (unless you're a bride-to-be throwing up in a gutter, in which case the details might be a little hazy).

• Anna Stothard's novel The Pink Hotel(Alma Books, £7.99) is on the longlist for the Orange Prize. To order a copy for £5.99 with free UK p&p, click on the link or call 0330 333 6846